# The sum on two numbers in 28...

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• Feb 28th 2007, 03:50 PM
ceasar_19134
The sum on two numbers in 28...
The sum of two numbers is 28 and their product is seven. Find the sum of the reciprocals of the numbers.

This one has me confused. How can their product equal 7 if 7 is prime?
1+27 027 14+14 196
2+26 052 13+15 195
3+25 075
• Feb 28th 2007, 04:05 PM
Plato
This is just a very basic algebra problem.
x+y=28
xy=7

(1/x)+(1/y)=?
• Feb 28th 2007, 04:36 PM
Soroban
Hello, ceasar!

Quote:

The sum of two numbers is 28 and their product is seven.
Find the sum of the reciprocals of the numbers.

This one has me confused.
How can their product equal 7 if 7 is prime?
WHO said these are whole numbers ??

There is a marvelously sneaky trick for this one . . .

We have: .x + y .= .28 . [1]
. . . . . . . . .xy . = . .7 . .[2]

Divide [1] by [2]: . x + y . . .28
. . . . . . . . . . . . . ------- .= .---
. . . . . . . . . . . . . . .xy . . . . 7

. . . . . . . . . . . x . . .y
And we have: .--- + --- .= .4
. . . . . . . . . . .xy . . xy

- - - . . . . . .1 . . 1
Therefore: - -- + -- .= .4 . . . . ta-DAA!
- - - . . . . . .y . . x